# Thread: series 1 - 1/2 -1/3 + 1/4 + 1/5 - 1/6 -1/7...

1. ## series 1 - 1/2 -1/3 + 1/4 + 1/5 - 1/6 -1/7...

Hello!

First, thanks for all the wonderful help during this course of Real Analysis! This website is amazing!

I have to determine whether the series: 1 - 1/2 -1/3 + 1/4 + 1/5 - 1/6 -1/7 + 1/8 + 1/9 - 1/10 - 1/11 ... converges or diverges

I assume I have to do a rearrangement to show this, but I don't know how.
Please, give me some hints

thanks

2. Originally Posted by inthequestofproofs
Hello!

First, thanks for all the wonderful help during this course of Real Analysis! This website is amazing!

I have to determine whether the series: 1 - 1/2 -1/3 + 1/4 + 1/5 - 1/6 -1/7 + 1/8 + 1/9 - 1/10 - 1/11 ... converges or diverges

I assume I have to do a rearrangement to show this, but I don't know how.
Please, give me some hints

thanks
Alternating series test - Wikipedia, the free encyclopedia

Edit: Sorry, I read your question wrong.

3. Okay so that is the sum to infinity of $\displaystyle (-1)^{n+1}\left(\frac{1}{n}\right)$ so look to see if this converges absolutely

4. The series can be written as...

$\displaystyle S= 1 + \sum_{n=1}^{\infty} (-1)^{n} (\frac{1}{2n} + \frac{1}{2n+1})$ (1)

.. so that is an alternating sign series whose terms are decreasing with n and tend to 0 if n tends to infinity: the series converges...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

5. BTW: you can only rearrange the terms if the series converges absolutely.

,
,

,

,

,

,

,

,

,

,

,

,

,

,

# determine convergent or divergent for given series 1-1/3 1/5-1/7 1/9

Click on a term to search for related topics.